Only if the transformer is non-ideal and one or two of the 3 sets of windings differs significantly from the others. [Edit: I see you addressed this in post #46, which I had missed.] Which might be true. But the voltage measurements in post #37 (which I assume are under no-load conditions) do not strongly suggest that.
I guess if the transformer is loaded unevenly, and you take measurements under load, then rolling the supply could help by matching the load imbalance to the supply imbalance.
Cheers, Wayne